Feeling Annoyed

Explanation

きもい

Reduction of 「きもちわるい(feel bad)」.
Direct translation is: "feel bad”but in this case, means: I can not accept him physically/mentally.
For example, she hates him, she doesn’t want to to talk or be seen together,
to the extent that she doesn’t even want to share the same breath of air with him as he is ugly or something.

That guy looking at us all the time, it's just weird.
あの男ずっと私たちを見てるよ、きもい～。

うざい

means うっとうしい(Annoying/Troublesome)
It feels like, you feel annoyed because something(someone) follows/goes after you and you don't want it/them.

In this case, for example:
There are some bugs flying around of my head and it is annoying
あたまの周りを飛んでる虫がうざい

My hair fringe is too long, I want to cut it because it makes me annoyed.
前髪が長すぎてうざいから切りたい

I can't see, don't stand in front of me! you are annoying...
見えないから前に立たないで、うざいなあ。

おやじ

It originally meant お父さん(father).
Basically this is a an informal expression to address your father but sometimes young girls use it too.
But outside of home, it refers to "a middle age guy(around 30 or 40-50 or 60 years old).".

There is strange middle-aged guy there.
あそこに変なおやじがいる。

This middle aged guy is ugly.
このおやじきたない。

モテモテ

It is モテる which means popularity, like, several people are attracted ,(like/love), to this person.
and モテモテ is an exaggerated form of モテる.(モテる is a verb and I dont know a parts-of-speech of モテモテ...)

I was very popular when I was a high school student.
高校生の頃はモテた（モテモテだった）

～じゃん

In this case, it means 「～だね」
But this word has a lot of expression. Usually it is put at the end of a phrase.